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Solve x 2 + 8x -12 = 0 by completing the square x 2 + 8x =12 x 2 + 8x + 16 =12 + 16 (x + 4) 2 =28 x + 4 = +  28 { -4 +2  x=-4 +2 

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Presentation on theme: "Solve x 2 + 8x -12 = 0 by completing the square x 2 + 8x =12 x 2 + 8x + 16 =12 + 16 (x + 4) 2 =28 x + 4 = +  28 { -4 +2  x=-4 +2 "— Presentation transcript:

1 Solve x 2 + 8x -12 = 0 by completing the square x 2 + 8x =12 x 2 + 8x + 16 = (x + 4) 2 =28 x + 4 = +  28 {  x=-4 +2 

2 6.3: Relationship of Roots, Factoring, Graphing & Solving Equations

3 If A*B = 0 then A= 0 or B = 0

4 (x+2) (x-3) = 0 (x+2)=0 or (x-3) = 0 x= -2 or x=3 Solve by factoring: x 2 – x - 6= 0 {-2, 3}

5 x 2 – x - 6= 0 Factors: Solutions: Roots: Graph: (x+2) (x-3) { -2,3} -2 and 3 x-int at -2 and 3 Equation:

6 Factors: Solutions: Roots: Graph: p and q {p, q} (x-p)(x-q) x-int at p and q Equation: MULT. and make it = 0

7 Solve by Factoring: 2x 2 +7x = 15 2x 2 +7x – 15 = 0 (2x-3) (x+5) = 0 (2x-3)=0 or (x+5)= 0 2x=3 or x=-5 x=3/2 or x=-5

8 Solve by Factoring: 5x 2 – 60=5x 5x 2 - 5x – 60 = 0 5(x 2 - x – 12) = 0 5(x-4) (x+3)= 0 5=0 x-4=0 or x+3= 0 x=4 or x=-3

9 Factors: Solutions: Roots: Graph: {0, –5 } Equation: 0 and -5 x(x+5) x 2 + 5x = 0 x-int at 0 and -5

10 Write two equations that has roots of ½ and –3/4 (x – ½) (x + 3/4 ) =0 x 2 + 3x/4 – x/2 – 3/8 = 0 8x 2 + 2x – 3 = 0 x 2 + 1x/4 – 3/8 =

11 Find two consecutive odd integers whose product is 195 x (x+2) = 195 x 2 + 2x = 195 x 2 + 2x – 195 = 0 (x-13)(x+15) =0 x-13 = 0 or x+15 =0 x=13 x= & 15 or -15 &-13

12 Factor by graphing: 2x 2 +7x x 2 +7x – 15 =y Roots: 3/2 and -5 Factors: (x – 3/2) (x+5) (2x – 3) (x + 5) Check: 2x 2 +7x - 15

13 Factor by graphing: 4x x =y Roots: 5 and -5 Factors: (x – 5) (x+5) 4(x – 5) (x + 5) Check: x 2 – 25 NO!


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